1. Compute the following: f sin²(x) dx

Q: Find an equation of the tangent plane to the given surface at the specified point. z = y cos(x - y),…

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Q: Letf(x) = x² – 5x + 6, g(x) = 5x – 1, find the following: (1)(f + g)(x) = (2) (ƒ − g)(x) = - (3) (ƒ…

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Q: Question 15 Given ƒ (2) - This function is discontinuous at the point A O z=0 x = -2 O=12 O == 2 <…

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Q: A function F(x) has a given value F(0) = 2. A graph of the derivative F'(x) is given below. What is…

A: A function F(x) has a given F(0)=2 A graph of derivatives F'(x) is given here .we find the value of…

Q: What is the average rate of change of the function f(t) = t² - 7t between t = -5 and t = -4? -16 -14…

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Q: Consider the following. y = x² y = 12 - x K 16 14 12 -2 10 B 6 4 2 2 8 10 12 (a) Find the area of…

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Q: Find ¹ d dx 1.8 √x -4,2x²2 +7x).

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Q: f '(t) = 10 cos(t) + sec2(t),    −?(pi)/2 < t < ?(pi)/2,    f(pi/3) = 4 find f

A: Taking anti-derivative,

Q: Determine the area of the shaded region in the following figure. The area of the shaded region is…

A: We have to find area

Q: The integrand of the definite integral is a difference of two functions. Sketch the graph of each…

A: This is a problem related to integration. Please find the general procedure given below.

Q: Use the graph below to fill in the missing values. -1 4 3 2 1 -1 f(0) f(x) K = 1 2 3 4 f(x)=0, x=…

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Q: 1) [2 Consider the DE: 15x²y + 3x³y - 24y = 0. A) Solve the given differential equation by…

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Q: Given that f(x) = x² 8x and g(x) = x + 15, find (a) f + g= (b) f-g= (c) fg= f (d) and its domain is…

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Q: Suppose f(x) √₂+² = √1+tdt 2x find f'(1).

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Q: ra a²-y² L". Sve²=v² a²-x²-y² . (x²z+y²z + z³) dzdxdy a²-x²-y²

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Q: Find the area of the region inside one leaf of the three-leaved rose r = cos 30. The area of the…

A: We have to find the area of the region inside one leaf of the three-leaved rose.

Q: Question 3 of 10 ♫ lim f(x)=-1 -2 Given find the following limit 3/7f(x)-g(r)² g(x)+1 and lim g(x)=1…

A: The given data is: limx→2fx=-1limx→2gx=1  Use the property of the limits to find the value of the…

Q: = [₁ rx Let I= f(x) dx, where fis the function whose graph is shown. y 12 8 4 1 2 (a) Use the graph…

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Q: Find lim lim h→0 h→0 f(5+h)-f(5) h f(5+h)-f(5) h = if f(x)=x² +5. (Simplify your answer.) ...

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Q: Two hours after the start of a 100-kilometer bicycle race, a cyclist passes the 82-kilometer mark…

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Q: For the given functions f(x) (1) (fog)(x) = (2) (gof)(x) = (3) (ƒ ○ f)(x) = (4) (gog)(x) = = 8x + 5,…

A: Let's find all given function.

Q: Which of the following statements must be true? 1. If f is differentiable, then II. If f is…

A: Solution of given question is written in below steps.

Q: A spherical rubber balloon is inflated with air. The volume of the spherical balloon of radius r…

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Q: Find the points of inflection of the graph of the function. (If an answer does not exist, enter…

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Q: For f(x)=x4 - 2x2 +6 find the following. (A) f'(x) (B) The slope of the graph off at x = 3 (C) The…

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Q: Find h'(t) if h(t)= h'(t)= 3 1/2 3 3/5

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Q: Determine the area of the shaded region bounded by y=-x² + 10x and y=x² - 6x.

A: Follow the procedure given below.

Q: The integral 9 [² 1 x - 1 dx

A: NOTE: Refresh your page if you can't see any equations. .

Q: Determine the solution y2(2) of the differential equation, given that it is satisfied by the…

A: Given :x2y''-xy'+y=0

Q: Which of the following statements is FALSE? O If the tangent line of a curve at a point is is a…

A: If the tangent line of a curve at a point is vertical line then its slope is infinite.

Q: To evaluate the integral 3 100+ x² dx, which of the following substitution be used? Select one: Ox=…

A: Topic:- application of integration

Q: Use an appropriate test to determine whether the series given below converges or diverges. 00 Σ n=1…

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Q: Question 3 (a) (b) Find the area of the region bounded by the curves y = x²(x ≥ 0), y = x² (x ≥ 0)…

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Q: The area A = ² of a circular oil spill changes with the radius. At what rate does the area change…

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Q: Use the four-step process to find f'(x), and then find f'(1), f'(2), and f'(3). f(x) = 4+7√√x f'(x)…

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Q: the answer is 3+6N but i dont know why, so please go step by step/explain how you get that answer.

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Q: Find the area inside one loop of the lemniscate r² = 2 sin 20. The area inside one loop of the…

A: Area of a closed region in polar coordinate is given by A=∬rdrdθ see below the answer and…

Q: lim 1-26 2 (2 + 3n-4n²) (1-2n + 3n²)

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Q: Evaluate the line integral [x(1 с where C is given by the line r(t) = (1 + 3t, 2t), 0≤ t ≤ 1. x(1 +…

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Q: Use the four-step process to find f'(x) and then find f'(1), f'(2), and f'(3). 9 X f(x) = 9+ f'(x) =…

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Q: Show that the differential form in the integral is exact. Then evaluate the integral. (1,2,3)…

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Q: each of the following cases, find the area of the region that lies inside both the curves. a) r= 1,…

A: Please see the below picture for detailed solution.

Q: Suppose that a sequence {an} is defined by the equations 1 = Which of the following is true about…

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Q: na Tic-Tac-Toe game, which player is assured of a win? Second Player There is no way of knowing.…

A: in a tic-tac-toe game , either first player can win game or second player can win game. Win will be…

Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F and…

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Q: Let f(x) = 9x² + 2x, g(x) = 7x - 7. Evaluate the following: (1) (f+g)(-3) = (2) (ƒ − g)( − 1) = -

A: First I have calculate the values of , f(-3),g(-3) , f(-1) and g(-1) then find the required values.…

Q: Find the areas of the regions enclosed by the following curves. (a) r = 1+2cosł

A: Given curve, r=1+2cos(θ) For range let r=1+2cos(θ)=02cos(θ)=-1cos(θ)=-12⇒θ=2π3

Q: π S xsin xdx

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Q: Question 29 Determine an equation for the line tangent to y² = x³ = x + 1 at (1, 1). Oy=-x y = x ° y…

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Q: Q[1]: Given the function shown below, evaluate the following: (a) lim f(x) x-2' (b) lim f(x) x-0 (c)…

A: Graph of the function f(x) is given, we have to find the limit at x=-2, x=0 and x=2